I have one of those reels and just took it apart. It has a simple click and pawl system inside. I turned the little plastic triangles and put it back together. It made it silent, but lost any anti-reverse or drag that it has. I put it back to its original position because I'm not willing to make that trade. I don't think there is a way to do it, although someone else may know better.

A click on a reel is a throwback to still fishing with bait. It let you go to sleep while you waited for a "bite". It is an abomination on a modern fly reel. I do a lot of night fishing here in Michigan, and a click will wake up every dog in the county. That wakes up the dogs' owners who imagine burglars, poachers, and such. Soon you find yourself standing in the middle of a stream with a spotlight in in your face. Then you know what a jacklighted deer must feel like just before the end. I modify Pfleuger Medalists to make them silent, both on retrieve and on stripping. They are cheap, work well, and are all the reel you need for trout fishing. The modification is a little complicated to describe here. It involves a change in the drag system, and can be done in 20 minutes. There is a minor disadvantage in that the drag ends up working in both directions, but do you reel in line so often that it really bothers you to have to reel against the drag?

I guess I should have answered redhotchillipepper's question in my first post. Yes, I once made one of those Hardy-type drags with the little triangles silent. I turned the triangles like shultzy501, and then packed the whole thing with really heavy wheel bearing grease. Aside from the fact that the drag worked both ways, it was O.K. However, I wanted it for night fishing. I don't know what would happen if you left a reel modified like that out in the sun!